The sum of the measures of the interior angles of a polygon is 720°. How many sides does the polygon have?
Mathematics · Middle School · Tue Nov 03 2020
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Given the statement:
The sum of the measures of the interior angles of a polygon is 720°.
Determine how many sides does the polygon has.
Solution:
We all know that the a hexagon with 6 sides has an interior angle sum of 720 degrees, hence, this can be solved using the formula.
S = (n − 2) × 180°
S = Sum of the interior angles
n = number of sides
Solve for n.
Divide both sides by 180°.
720° = (n − 2) × 180°
720°/180° = (n − 2) × 180°/180°
4 = n - 2
Transpose -2 to the other side of the equation, hence it must be taken to note that in transposing a number, the sign changes.
n = 4 + 2
n = 6
Final answer:
Number of sides = 6